You do realise the Daimyo is a paper tiger, and in the end, his approval means less than shit?
Tsunade would laugh in his face if he thought to actually press his opinion on who the next Hokage should be.
The Daimyo's are crucial in that they keep the rest of the country the village opperates in run smoothly- allowing them easy access to trade, and funding from missions he employs them on.
However, his successor will most likely prove much more co-operative than the current one. Thus, the toeing of line between each others authority. The villages let the daimyo run the country as he wills, and he lets them run the village as they like.
How the idea of the daimyo having power of any sort came to be continues to boggle my mind.
It's one of the worst plot points you can employ, simply for the cheapness of it- the 'big boss' who comes and issues orders that fuck the little guy.
When Naruto and Sasuke fought, Naruto had half of Kurama' chakra and had been fighting much longer than Sasuke. Sasuke in contrast, was draining power from 8 and a half biiju, was much fresher and still only came up even.
After, Naruto has access to all nine Biiju chakra, and enhanced regeneration provided by the Shodai's cells.
It should be no question who the Hokage should be- and the kage is always the strongest (or offered to the strongest [see Jiraiya]) which gives you strange things like a young third or the meathead that is the fourht Raikage.
Author's response
You do realize that truthfully you have no idea how much or little the Daimyo is a Paper Tiger based on the actual manga. After all, it was the Daimyo that selected Danzou as the Sixth Hokage, who if even your own theory was correct Naruto should have been the Hokage then based solely on his defeating Pain. I mean seriously, the idea that the village exists solely at the Daimyo's behest was first introduced in the Naruto movie, Inheritor of the Will of Fire, where he threatened to destroy the village if they didn't deal with Hiruko. Now that is a filler example, would you like a canon one okay see below.
If you read the story, you'd also realize that one of the first items I established was that those powers faded. Granted I still believe Naruto is stronger, but strength alone should never be used to determine who is Hokage. After all, I tend to believe Shikamaru would be a far better Hokage then Naruto as presented in canon. Because, while Naruto was busy giving not a shit about the morale of the army, Shikamaru rallied them. Naruto as you describe him might be strong, but that doesn't make him a leader of men. Which a Hokage is.
But again, if the Daimyo was just a pushover as you claim then how do you explain Danzou. A crippled warrior who as he presented himself to the village was nowhere near his prime when he was selected as Hokage. Granted he used mind control on the DAimyo, but Shikaku was against it and yet Danzou was still made Hokage solely on the Daimyo's decision and it would be confirmed based on a vote of the jounin. Please base your opinions off of facts shown in the manga before proclaiming Naruto deserves everything just because he is strong. The Hokage is as much a political position or one based on popularity of the candidates as it is one earned by merit of strength.
I guess one other point I want to raise is that based solely on the Danzou example I gave, it would seem that I used the Daimyo exactly as Kishimoto did. Now, that might not do much to dispute it being one of the worst plot points one could use, especially as Kishimoto turned out to be a pretty cruddy writer. But, considering he brought the Daimyo in to pick Danzou as there was likely no other way for him to become Hokage, you could say the way the Fire Daimyo used in The Pride to install Sasuke is exactly the same as he was used in canon.
Not to mention your point about strength is irrelevant considering after the war Kakashi became Hokage not the supposedly strongest Naruto. That didn't happen till years later.